Rotor position estimation apparatus and methods

ABSTRACT

Motor drives, methods and estimation systems are presented for estimating a rotor position of a motor load in which four sets of inverter output current samples obtained at four different sample times in a given inverter PWM cycle are converted into a corresponding stationary reference frame current value pairs, and the rotor position estimate is computed according to the stationary reference frame current values.

TECHNICAL FIELD

The subject matter disclosed herein relates to power conversion, andmore specifically to rotor position estimation apparatus and techniquesfor motor drive power converters.

BRIEF DESCRIPTION

Various aspects of the present disclosure are now summarized tofacilitate a basic understanding of the disclosure, wherein this summaryis not an extensive overview of the disclosure, and is intended neitherto identify certain elements of the disclosure, nor to delineate thescope thereof. Rather, the primary purpose of this summary is to presentvarious concepts of the disclosure in a simplified form prior to themore detailed description that is presented hereinafter. The presentdisclosure provides motor drives, estimation systems therefor andmethods for estimating a motor load rotor position in which four sets ofinverter output current samples obtained at four different sample timesin a given inverter PWM cycle are converted into a correspondingstationary reference frame current value pairs and the rotor positionestimate is computed at least partially according to the stationaryreference frame current values.

BRIEF DESCRIPTION OF THE DRAWINGS

The following description and drawings set forth certain illustrativeimplementations of the disclosure in detail, which are indicative of oneor more exemplary ways in which the various principles of the disclosuremay be carried out. The illustrated examples are not exhaustive of themany possible embodiments of the disclosure. Various objects, advantagesand novel features of the disclosure will be set forth in the followingdetailed description when considered in conjunction with the drawings,in which:

FIG. 1 is a schematic system diagram;

FIG. 2 is a graph;

FIG. 3 is a schematic diagram;

FIG. 4 is a flow diagram; and

FIG. 5 is a graph.

DETAILED DESCRIPTION

FIG. 1 illustrates a power conversion system 2 including a motor drive10 with an input rectifier 20 having AC input lines R, S and T receivingmultiphase AC input power from a source 4. The rectifier 20 provides DCoutput power via first and second DC output nodes or terminals (e.g.,DC+ and DC−) to an intermediate DC link circuit 30 including a DC linkcapacitance C. The motor drive 10 further includes an output inverter 40receiving DC input power from the DC link circuit 30, where the inverter40 includes IGBTs or other inverter switching devices individuallycoupled between a corresponding DC link circuit node and a correspondingone of three AC output nodes or terminals U, V and W. Any suitableinverter switching devices may be used, including without limitationinsulated gate bipolar transistors (IGBTs), silicon controlledrectifiers (SCRs), gate turn-off thyristors (GTOs), integrated gatecommutated thyristors (IGCTs), etc. The inverter switching devices areoperated according to inverter switching control signals 46 from aninverter controller 42 in order to convert DC power from the linkcircuit 30 to provide multiphase, variable frequency, variable amplitudeAC output power to drive an associated motor load 6 coupled with theoutput inverter 40 of the motor drive 10 via a cable 8.

The various aspects of the present disclosure are hereinafter describedin connection with a three-phase output inverter 40, although differentembodiments are contemplated involving more than three output phases todrive an AC motor load 6. As seen in FIG. 1, the motor drive 10 receivesmultiphase AC input power from a three-phase source 4, althoughembodiments are possible using single-phase input power and/ormultiphase input power from a source 4 having more than three phases. Inthe illustrated embodiment, moreover, a passive rectifier circuit 20 isincluded in the illustrated motor drive 10, although otherimplementations are possible in which a motor drive system 10 receivesDC input power from an external source and/or where an active rectifier20 is used. In addition, the illustrated motor drive 10 is a voltagesource converter architecture having a DC bus circuit connected to, theoutput terminals of the rectifier 20, with the capacitance C connectedbetween the positive and negative DC bus terminals DC+ and DC−, althoughother embodiments are possible in which a current source converterconfiguration is used, for example, having an intermediate DC linkcircuit 30 providing a regulated DC link current to the inputs of theinverter 40, and the DC link circuit 30 may include one or more DC linkchokes or inductances (not shown). As further shown in FIG. 1, the cable8 provides an impedance including inductance and capacitance between theoutput of the inverter 40 and the driven motor 6, and variousimplementations of a motor drive system 2 may include an output filtersand/or transformers (not shown) coupled between the motor drive 10 andthe motor load 6.

The inverter switching devices are individually connected between one ofthe DC bus terminals DC+ and DC− and the corresponding AC output phaseU, V or W, and are operative according to a corresponding one of aplurality of switching control signals 46 from the inverter controller42 in order to selectively electrically connect or disconnect thecorresponding DC terminal to/from the corresponding AC output line. Inpractice, the controller 42 provides inverter switching control signals46 to the corresponding inverter switches in a manner suitable forconversion of the input DC electrical power to variable frequency,variable amplitude AC output power suitable for controlling operation ofthe connected motor load 6. In this regard, the inverter controller 42provides the switching control signals 46 in order to implement adesired control strategy, for example, control or regulation of themotor operation according to one or more setpoint inputs (not shown),such as a desired motor speed, torque, position, etc., and thecontroller 42 may employ one or more feedback signals to implement thecontrol strategy in a closed loop fashion. In this regard, the motordrive 10 includes current sensors providing inverter output currentfeedback signals or values 54 to the inverter controller 42, and theillustrated controller 42 includes or implements an inverter controlcircuit or component 44, such as signal conditioning and drivercircuitry with associated logic circuits and/or programming of aprocessor 41 providing suitable switching control signals 46 forselectively operating the inverter switching devices, as well as anassociated non-transitory electronic memory storing data values andprogramming instructions.

In one embodiment, moreover, the control circuit or component 44implements closed loop control of the inverter 40 in order to controloperation of the driven motor load 6 at least partially according to anestimated rotor position angle θ 52 using a sine-triangle pulse widthmodulation technique in which a desired inverter output parameter (e.g.,output voltage command signal or value) for each output phase U, V and Wis compared with a corresponding triangle wave carrier 48 to determinethe desired on or off state for the inverter switching devicesassociated with each given phase. The modulation can be implemented inhardware using comparators, triangle waveform generators, etc. and/orcomparison of the carrier 48 and desired output value for acorresponding inverter output phase may be implemented insoftware/firmware executed by the processor 41, with the correspondingcarrier waveforms 48 being stored in the electronic memory and/orotherwise implemented in processor-executed software and/or firmware.

The controller 42 and the components thereof can include suitable logicor processor-based circuitry and an electronic memory storing data andprogramming code, and may also include signal level amplification and/ordriver circuitry (not shown) to provide suitable drive voltage and/orcurrent levels via the signals 46 sufficient to selectively actuate theinverter switching devices, for instance, such as comparators, carrierwave generators or digital logic/processor elements and signal driversor combinations thereof. Moreover, the controller 42 can provide theswitching control signals 46 according to any suitable pulse widthmodulation (PWM) technique, including without limitation carrier-basedpulse width modulation, etc., which performs normal motor control tasks,including pulse width modulation operation of the inverter. switches.

Referring now to FIGS. 1-5, the inventors have appreciated that variousmotor drive applications involve somewhat lengthy cables 8 and/or otherintervening structures (e.g., transformers, filters, etc.) making directmeasurement of the position of the rotor difficult or impractical.Accordingly, the controller 42 further implements a rotor positionestimation system 50, which can be a separate circuit configured with asuitable electronic processor, or may be implemented by the invertercontroller processor 41 in certain embodiments.

A graph 60 in FIG. 2 illustrates phase shifted carriers 48 u, 48 v and48 w employed by the inverter controller 42 in generating the pulsewidth modulated inverter switching control signals 46 for the AC outputphases U, V and W, respectively, where the carriers 48 are phase shifted120° relative to one another as shown in the graph 60 in one embodiment.In this manner, high frequency signals are inserted into the AC outputpower delivered to the motor load 6 at a frequency generallycorresponding to the inverter pulse width modulation frequency. Thephase shifting of the carriers 48 need not be exactly 120°, for example,where the phase shifting is generally 360°/X, where X is an integercorresponding to the number of output phases provided by the inverter40. Moreover, phase shifting within one or two or several degrees of120° may be used, with the ultimately estimated rotor position beingoffset based on the difference between the carrier phase shifting and120°. The illustrated embodiments provide triangular carrier waveforms,although other embodiments are possible using carriers of differentwaveform shapes, and the concepts of the present disclosure are notlimited to implementations using triangular carrier waveforms.Furthermore, the carriers 48 and the use thereof in generating pulsewidth modulated switching control signals 46 to operate the inverter 40can be implemented using any suitable modulation technique, wherein thecarriers 48 can be implemented using analog circuitry, lookup tables,parametric equations, or other suitable techniques or combinationsthereof.

The graph 60 in FIG. 2 further illustrates several example inverter PWMcycles having a corresponding PWM period T_(PWM). In one possibleimplementation, the PWM frequency employed by the inverter controller 42is in the range of 1 kHz or more, although the concepts of the presentdisclosure can be employed in association with any suitable PWMfrequency having a corresponding PWM period T_(PWM), and the PWMswitching frequency may be fixed or adjustable in various embodiments.

FIG. 2 further provides a graph 62 illustrating example α-β stationaryreference frame PWM-frequency voltages v_(αh) and v_(βh) applied to themotor load 6, as well as a graph 64 showing α-β stationary referenceframe currents i_(αh) and i_(βh) corresponding to the u, v, w stationaryreference frame inverter output current signals or values 54 measured orsensed at the output of the inverter 40. As further seen in FIG. 2, therotor position estimation system 50 is provided with four sets ofinverter output current samples i_(uvw)(t_(i)) obtained at fourdifferent sample times (t₁, t₂, t₃, t₄) in a given inverter pulse widthmodulation cycle, and the system 50 uses these to estimate the rotorposition θ representing the angular position of the rotor of the drivenmotor load 6 as detailed further below.

The controller 42 obtains the inverter output current samples 54 usingany suitable sampling technique. For example, analog sensors can providephase current signals 54 to an analog to digital (A/D) converter (notshown) of the controller 42 which provides for conversions to generatecorresponding sample values at the sample times t₁, t₂, t₃ and t₄, wheremultiple converters may be used and/or sample and hold (S/H) circuitry(not shown) can be provided such that the phase currents i_(uvw)(t_(i))are obtained concurrently or approximately concurrently for each of theinverter output phases φ=U, V and W corresponding to the four differentsample times t₁, t₂, t₃ and t₄ in a given inverter pulse widthmodulation cycle. Moreover, as shown in the example of FIG. 2, the foursets of multiphase inverter output current samples i_(uvw)(t_(i)) areobtained or sampled approximately at 90° intervals in each giveninverter pulse width modulation cycle.

In various implementations, the sampling may be somewhat skewed, with ashared A/D converter in certain implementations sampling and convertingsignals 54 from the phase current sensors serially using a multiplexer,etc., whereby the samples need not be obtained exactly at 90° intervalsin all embodiments. Any suitable sampling control configuration can beused, for example, with the processor 41 controlling the sampling byoperation of the conversion circuitry, with the processor 41 in certainembodiments also controlling the provision of the inverter switchingcontrol signals 46 and controlling the correspondence between theswitching control signal generation and the inverter output currentsampling. In certain embodiments, moreover, the current sensorsmeasuring the inverter output currents may provide digital values, withthe processor 41 controlling the timing of the sampling by operativeinterconnection with the current sensors. In this regard, the rotorposition estimation system 50 may be implemented by the processor 41,with logic of the estimation system 50 controlling the sampling of theinverter output current signals or values 54.

In the illustrated embodiment, moreover, the inverter output currentsampling is done in correspondence with one of the inverter outputcarriers 48, in this case, the carrier 48 u. As seen in FIG. 2, forexample, the sample times t₁, t₂, t₃ and t₄ correspond to approximatelythe peaks, valleys and mid-points of the carrier 48 u. Thus, thecarriers 48 themselves are offset from one another by 120° in theillustrated three-phase example, whereas the sampling times t₁, t₂, t₃and t₄ are offset by approximately 90° for the illustrated three-phaseimplementation, and the same sampling offset (approximately 90°) is usedin multiphase inverter output embodiments having more than three outputphases. Any suitable carriers 48 can be used having a peak, a valley andtwo midpoints generally equally approximately 90° in each PWM cycle ofthe inverter 40, including without limitation the illustrated triangularwaveforms 48 u, 48 v and 48 w, wherein the concepts of the presentdisclosure are not limited to the illustrated example carriers 48. Inoperation, the estimation system or component 50 estimates the motorrotor angular position θ by computations using stationary referenceframe current values shown in the graph 64 at the sample times t₁, t₂,t₃ and t₄, where the stationary reference frame current values arecomputed by the system 50 based on the sample signals or values 54i_(uvw)(t_(i)) obtained at the four sample times in a given PWM cycle.

The estimation system or component 50 in one embodiment provides anestimated rotor position signal or value θ in each PWM cycle, althoughthe estimation can be done less frequently in other embodiments. Inaddition, the estimated rotor position θ can be provided for use by theclosed loop control component 44 in generating the inverter switchingcontrol signals 46 (e.g., as feedback for position and/or speed controlor regulation functions) and/or the position can be used for otherpurposes, including provision of a digital value and/or analog signal toan external system or network (not shown). Moreover, the illustratedexample provides the rotor position estimate θ as a digital value 52resulting from computations implemented by the processor 41, althoughother embodiments are possible in which the estimate θ can be providedby the system 50 as an analog signal or in another usable form.

In operation, the estimation system 50 converts four sets of multiphaseinverter output current samples i_(uvw)(t_(i)) for a given PWM cycle ofthe inverter 40 into four corresponding pairs of stationary referenceframe current values i_(α)(t_(i)), i_(β)(t) for each of the sample timest_(i)=t₁, t₂, t₃, t₄ using any suitable reference frame conversiontechnique, including without limitation the conversion or transformationexample illustrated in FIG. 5 below.

FIG. 3 schematically illustrates further details of one non-limitingimplementation of the rotor position estimation system or component 50,receiving the inverter output current samples 54 as signals or values(i_(uvw)), with a conversion circuit or component 70 providingconversion from the U, V, W reference frame to the stationary α-βreference frame to produce the four corresponding pairs of stationaryreference frame current values 72 (i_(αβ)(t₁), i_(αβ)(t₂), i_(αβ)(t₃)and i_(αβ)(t₄)). The system 50 computes numerator and denominatorsummations 74 to compute numerator and denominator values 76 as shown(numerator u(1)=−[i_(α)(t₂)−i_(α)(t₄)+i_(β)(t₁)−i_(β)(t₃)] anddenominator u(2)=[i_(β)(t₂)−i_(β)(t₄)−i_(α)(t_(i))+i_(α)(t₃)] in oneembodiment). Computation circuits or components 78 and 79 compute therotor position estimate value θ 52 according to the following equation(1):

$\begin{matrix}{\theta = {0.5\mspace{14mu} {{\tan^{- 1}\left( \frac{u(1)}{u\; (2)} \right)}.}}} & (1)\end{matrix}$

By this operation, the rotor position estimation system or component 50computes the estimated rotor position θ for a given inverter PWM cycleat least partially according to the stationary reference frame currentvalues i_(α)(t_(i)), i_(β)(t_(i)) for that PWM cycle. Moreover, as thecontroller 42 provides the inverter PWM switching control signals 46using phase shifted carriers 48 for the inverter output phases U, V andW, the resulting high frequency signal content (e.g., at the inverterPWM switching frequency) facilitates computation of the rotor positionestimate θ without requiring encoders or other position sensors at themotor load 6, and without measuring motor currents or voltages on theload side of the cable 8. Moreover, the techniques of the presentdisclosure advantageously use only four samples of the inverter outputcurrents 54 in a given PWM cycle of the inverter 40, and utilize simplemathematical operations for the computed numerator and denominatorvalues 74, 76, providing computational advantages compared with otherposition estimation techniques.

FIG. 4 depicts a process or method 80 for estimating a rotor position θof a motor load 6 driven by an inverter 40, which may be implementedusing the estimation system 50 of FIGS. 1 and 3 in one embodiment.Although the method 80 is illustrated and described below in the form ofa series of acts or events, it will be appreciated that the variousmethods or processes of the present disclosure are not limited by theillustrated ordering of such acts or events. In this regard, except asspecifically provided hereinafter, some acts or events may occur indifferent order and/or concurrently with other acts or events apart fromthose illustrated and described herein in accordance with thedisclosure. Furthermore, not all illustrated steps may be required toimplement a process or method in accordance with the present disclosure,and one or more such acts may be omitted and/or combined. Theillustrated methods and other methods of the disclosure may beimplemented in hardware, processor-executed software, processor-executedfirmware, programmable logic, etc. or combinations thereof, in order toprovide rotor position estimation functionality described herein, andmay be employed in any power conversion system including but not limitedto the above illustrated motor drive 10, wherein the disclosure is notlimited to the specific applications and embodiments illustrated anddescribed herein. Moreover, the present disclosure involvesnon-transitory computer readable mediums, such as an electronic memoryof the controller 42 in FIG. 1, having computer executable instructionsfor implementing the various rotor position estimation processes andmethods described herein, including the process 80 of FIG. 4.

The flow diagram of FIG. 4 illustrates an exemplary PWM cycle duringoperation of the motor drive, wherein the position estimation aspects ofthe process 80 may be implemented in all inverter PWM cycles, orselectively in less than all such PWM cycles in various embodiments. At82 in FIG. 4, the controller 42 provides inverter PWM switching controlsignals 46 for the current or present PWM cycle using three carriers 48that are phase shifted at 120° relative to one another in order tointroduce high-frequency signals or components for sensorless rotorposition estimation. At 84, the controller 42 (e.g., the processor 41implementing the rotor position estimation component or system 50 in oneexample) samples the inverter output currents 54 at four differentsample times t₁, t₂, t₃ and t₄ during the present PWM cycle. In theillustrated embodiment, for example, the inverter output currents 54 aresampled at 84 at 90° intervals of the 360° duration of the current PWMcycle. In addition, the sampling in certain embodiments (e.g., FIG. 2above) is correlated with one of the phase-shifted carriers 48, such ascarrier 48 u, with the samples being obtained approximately at thepeaks, valleys and midpoints of the selected carrier 48 u in the givenPWM cycle. Thus, at each sampling time t₁, t₂, t₃ and t₄, a set of threeinverter output current signals or values 54 is obtained at 84.

Referring also to FIG. 5, the four sets of three samples 54 for thecurrent PWM cycle are converted at 86 in FIG. 4 in order to provide fourpairs of α-β stationary reference frame current values i_(α)(t_(i)),i_(β)(t_(i)) for i=1, 2, 3 and 4. FIG. 5 illustrates one suitablestationary reference frame conversion process which may be employed forthe conversion at 86, in which a graph 92 shows an u, v, w referenceframe with an overlay of the α-β stationary reference frame, and thestationary reference frame current values i_(α)(t_(i)), i_(β)(t_(i)) arecomputed according to the following equations (2) and (3) (e.g., shownat 94 and 96 in FIG. 5):

$\begin{matrix}{{i_{\alpha \; \beta \; 0} = {T_{{uvw}\rightarrow{\alpha \; \beta \; 0}} \cdot i_{uvw}}},{where}} & (2) \\{T_{{uvw}\rightarrow{\alpha \; \beta \; 0}} = {{\frac{2}{3}\begin{bmatrix}1 & {- \frac{1}{2}} & {- \frac{1}{2}} \\0 & \frac{\sqrt{3}}{2} & {- \frac{\sqrt{3}}{2}} \\\frac{1}{2} & \frac{1}{2} & \frac{1}{2}\end{bmatrix}}.}} & (3)\end{matrix}$

Thereafter at 88 in FIG. 4, the estimated rotor position θ is computedaccording to the four pairs of stationary α-β reference frame valuesobtained at 86 (e.g., using the above equation (1)). Thereafter at 90,the next PWM cycle begins, with the process 80 returning to 82-88 asdescribed above.

The inventors have appreciated that the voltages v_(α) and v_(β) of apermanent magnet (PM) motor in the a-β stationary reference frame are asfollows:

${\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix} = {{R \cdot \begin{bmatrix}i_{\alpha} \\i_{\beta}\end{bmatrix}} + {\begin{bmatrix}{L_{0} + {L_{1}\mspace{14mu} \cos \; 2\; \theta}} & {L_{1}\mspace{14mu} \sin \; 2\; \theta} \\{L_{1}\mspace{14mu} \sin \; 2\; \theta} & {L_{0} - {L_{1}\mspace{14mu} \cos \; 2\; \theta}}\end{bmatrix}{\frac{}{t}\begin{bmatrix}i_{\alpha} \\i_{\beta}\end{bmatrix}}} + {\left( {\frac{}{t}\begin{bmatrix}{L_{0} + {L_{1}\mspace{14mu} \cos \; 2\; \theta}} & {L_{1}\mspace{14mu} \sin \; 2\; \theta} \\{L_{1}\mspace{14mu} \sin \; 2\; \theta} & {L_{0} - {L_{1}\mspace{14mu} \cos \; 2\; \theta}}\end{bmatrix}} \right).\begin{bmatrix}i_{\alpha} \\i_{\beta}\end{bmatrix}} + {\omega \; {\lambda_{pm}\begin{bmatrix}{{- \sin}\; \theta} \\{\cos \; \theta}\end{bmatrix}}}}}, {{{where}\mspace{14mu} L_{0}} = \frac{L_{q} + L_{d}}{2}},{L_{1} = {\frac{L_{d} - L_{q}}{2}.}}$

L_(q) is the torque-axis (q-axis) self inductance, and L_(d) is theflux-axis (d-axis) self inductance.

The carrier frequency components are given as follows:

$\begin{bmatrix}v_{\alpha \; h} \\v_{\beta \; h}\end{bmatrix} = {{\begin{bmatrix}{L_{0} + {L_{1}\mspace{14mu} \cos \; 2\; \theta}} & {L_{1}\mspace{14mu} \sin \; 2\; \theta} \\{L_{1}\mspace{14mu} \sin \; 2\; \theta} & {L_{0} - {L_{1}\mspace{14mu} \cos \; 2\; \theta}}\end{bmatrix}{\frac{}{t}\begin{bmatrix}i_{\alpha \; h} \\i_{\beta \; h}\end{bmatrix}}} = {L \cdot {{\frac{}{t}\begin{bmatrix}i_{\alpha \; h} \\i_{\beta \; h}\end{bmatrix}}.}}}$

Defining the carrier frequency voltages in the α-β stationary referenceframe as follows:

${\begin{bmatrix}v_{\alpha \; h} \\v_{\beta \; h}\end{bmatrix} = {V_{h}\begin{bmatrix}{\cos \mspace{14mu} \omega_{h}t} \\{\sin \mspace{14mu} \omega_{h}t}\end{bmatrix}}},$

where “ω_(h)” is the carrier frequency component, the α-β referenceframe currents are given by the following:

${\begin{bmatrix}i_{\alpha \; h} \\i_{\beta \; h}\end{bmatrix} = {{L^{- 1}{\int\begin{bmatrix}v_{\alpha \; h} \\v_{\beta \; h}\end{bmatrix}}} = {{\frac{V_{h}}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}\begin{bmatrix}{L_{0} - {L_{1}\mspace{14mu} \cos \; 2\; \theta}} & {{- L_{1}}\mspace{14mu} \sin \; 2\; \theta} \\{{- L_{1}}\mspace{14mu} \sin \; 2\; \theta} & {L_{0} + {L_{1}\mspace{14mu} \cos \; 2\; \theta}}\end{bmatrix}} \cdot \begin{bmatrix}{\sin \mspace{14mu} \omega_{h}t} \\{{- \cos}\mspace{14mu} \omega_{h}t}\end{bmatrix}}}},{where}$${{i_{ah} = \frac{V_{h}\left\lbrack {{{\left( {L_{0} - {L_{1}\mspace{14mu} \cos \; 2\; \theta}} \right) \cdot \sin}\mspace{14mu} \omega_{h}t} + {L_{1}\mspace{14mu} \sin \; 2\; {\theta \cdot \cos}\mspace{14mu} \omega_{h}t}} \right\rbrack}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}},{and}}\;$$i_{\beta \; h} = \frac{- {V_{h}\left\lbrack {{L_{1}\mspace{14mu} \sin \; 2\; {\theta \cdot \sin}\mspace{14mu} \omega_{h}t} + {{\left( {L_{0} + {L_{1}\mspace{14mu} \cos \; 2\; \theta}} \right) \cdot \cos}\mspace{14mu} \omega_{h}t}} \right\rbrack}}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}$

The α-axis and β-axis current is detected at the peak and valley of acarrier (cos ω_(h)t=0) as follows:

${i_{\alpha} = {i_{\alpha \; f} \mp \frac{V_{h}\left( {L_{0} - {L_{1}\mspace{14mu} \cos \; 2\; \theta}} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}},{{{and}.\mspace{14mu} i_{\beta}} = {i_{\beta \; f} \pm \frac{V_{h}\left( {L_{1}\mspace{14mu} \sin \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}$

The α-axis and β-axis current is also detected at the mid points (sinω_(h)t=0) as follows:

${i_{\alpha} = {i_{\alpha \; f} \pm \frac{V_{h}\left( {L_{1}\mspace{14mu} \cos \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}},{{{and}\mspace{14mu} i_{\beta}} = {i_{\beta \; f} \mp {\frac{V_{h}\left( {L_{0} + {L_{1}\mspace{14mu} \sin \; 2\; \theta}} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}.}}}$

The difference between the α-axis and β-axis at cos ω_(h)t=0 is asfollows:

${{{{i_{\alpha}\left( t_{1} \right)} - {i_{\alpha}\left( t_{3} \right)}} = {i_{\alpha \; 1} = {- \frac{2\; V_{h}\left( {L_{0} - {L_{1}\mspace{14mu} \cos \; 2\; \theta}} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}}, {and}}\;$${{i_{\beta}\left( t_{1} \right)} - {i_{\beta}\left( t_{3} \right)}} = {i_{\beta \; 1} = \frac{2\; {V_{h}\left( {L_{1}\mspace{14mu} \sin \; 2\; \theta} \right)}}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}$

The difference between the α-axis and β-axis at sin ω_(h)t=0 is asfollows:

${{{{i_{\alpha}\left( t_{2} \right)} - {i_{\alpha}\left( t_{4} \right)}} = {i_{\alpha \; 2} = \frac{2\; {V_{h}\left( {L_{1}\mspace{14mu} \sin \; 2\; \theta} \right)}}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}, {and}}\;$${{i_{\beta}\left( t_{2} \right)} - {i_{\beta}\left( t_{4} \right)}} = {i_{\beta \; 2} = {- {\frac{2\; {V_{h}\left( {L_{0} + {L_{1}\mspace{14mu} \cos \; 2\; \theta}} \right)}}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}.}}}$

This yields the following formula for the rotor position θ (e.g.,equation (1) above):

${\theta = {0.5\mspace{14mu} {\tan^{- 1}\left( \frac{u(1)}{u(2)} \right)}}},{{where}\text{:}}$${{u(1)} = {{- \left( {i_{\alpha \; 2} + i_{\beta \; 1}} \right)} = {- \frac{4\; V_{h}\left( {L_{1}\mspace{14mu} \sin \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}}, {{u(2)} = {{i_{\beta \; 2} - i_{\alpha \; 1}} = {- \frac{4\; V_{h}\left( {L_{1}\mspace{14mu} \cos \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}},{and}$${k_{1} = \frac{{- 4}\; V_{h}L_{1}}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}},$

where k₁>0 for interior permanent magnet (IPM) motors 6.

As seen above, therefore, the estimation system or component 50advantageously provides position information for use in motor controlvia the controller 42 and/or for any other suitable usage in the drive10 and/or an external system or network at least partially according tothe four sets of multiphase inverter output current samples for a givenPWM cycle of the inverter 40.

The above examples are merely illustrative of several possibleembodiments of various aspects of the present disclosure, whereinequivalent alterations and/or modifications will occur to others skilledin the art upon reading and understanding this specification and theannexed drawings. In particular regard to the various functionsperformed by the above described components (assemblies, devices,systems, circuits, and the like), the terms (including a reference to a“means”) used to describe such components are intended to correspond,unless otherwise indicated, to any component, such as hardware,processor-executed software, or combinations thereof, which performs thespecified function of the described component (i.e., that isfunctionally equivalent), even though not structurally equivalent to thedisclosed structure which performs the function in the illustratedimplementations of the disclosure. In addition, although a particularfeature of the disclosure may have been disclosed with respect to onlyone of several implementations, such feature may be combined with one ormore other features of the other implementations as may be desired andadvantageous for any given or particular application. Also, to theextent that the terms “including”, “includes”, “having”, “has”, “with”,or variants thereof are used in the detailed description and/or in theclaims, such terms are intended to be inclusive in a manner similar tothe term “comprising”. This description uses examples to disclosevarious embodiments and also to enable any person skilled in the art topractice the disclosed subject matter, including making and using anydevices or systems and performing any incorporated methods. It will beevident that various modifications and changes may be made, andadditional embodiments may be implemented, without departing from thebroader scope of the present disclosure as set forth in the followingclaims, wherein the specification and drawings are to be regarded in anillustrative rather than restrictive sense.

The following is claimed:
 1. An estimation system for estimating a rotorposition of a motor load driven by an inverter, wherein the estimationsystem: converts each of four sets of multiphase inverter output currentsamples obtained at four different sample times in a given inverterpulse width modulation cycle into a corresponding pair of stationaryreference frame current values, and computes an estimated rotor positionfor the given inverter pulse width modulation cycle at least partiallyaccording to the stationary reference frame current values for the giveninverter pulse width modulation cycle.
 2. The estimation system of claim1, wherein the four sets of multiphase inverter output current samplesare sampled approximately at 90° intervals in the given inverter pulsewidth modulation cycle.
 3. The estimation system of claim 2, wherein thefour sets of multiphase inverter output current samples are sampledapproximately at peaks, valleys and mid-points of one of a plurality ofphase shifted carriers used in the given inverter pulse width modulationcycle to operate the inverter.
 4. The estimation system of claim 1,wherein the four sets of multiphase inverter output current samples aresampled approximately at peaks, valleys and mid-points of one of aplurality of phase shifted carriers used to operate the inverter in thegiven inverter pulse width modulation cycle.
 5. The estimation system ofclaim 1, wherein the estimation system: computes the estimated rotorposition θ for the given inverter pulse width modulation cycle accordingto α-β stationary reference frame current value pairs i_(α)(t_(i)),i_(β)(t_(i)) for the four sample times t_(i) where i=1-4 according tothe following equation:${{\theta = {0.5\mspace{14mu} {\tan^{- 1}\left( \frac{u(1)}{u(2)} \right)}}},{{where}\text{:}}}\mspace{11mu}$$\; {{{u(1)} = {{- \left( {i_{\alpha \; 2} + i_{\beta \; 1}} \right)} = {- \frac{4\; V_{h}\left( {L_{1}\mspace{14mu} \sin \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}}, {{u(2)} = {{i_{\beta \; 2} - i_{\alpha \; 1}} = {- \frac{4\; V_{h}\left( {L_{1}\mspace{14mu} \cos \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}}, {and}}\;$ i_(α1) = i_(α)(t₁) − i_(α)(t₃), i_(β 1) = i_(β)(t₁) − i_(β)(t₃), i_(α 2) = i_(α)(t₂) − i_(α)(t₄), andi_(β 2) = i_(β)(t₂) − i_(β)(t₄).
 6. The estimation system of claim5, wherein the four sets of multiphase inverter output current samplesare sampled approximately at 90° intervals in the given inverter pulsewidth modulation cycle.
 7. The estimation system of claim 5, wherein thefour sets of multiphase inverter output current samples are sampledapproximately at peaks, valleys and mid-points of one of a plurality ofphase shifted carriers used in the given inverter pulse width modulationcycle to operate the inverter.
 8. A motor drive, comprising: amultiphase inverter comprising a plurality of inverter switching devicesindividually coupled between an inverter DC input and a multiphaseinverter AC output; a controller providing pulse width modulatedswitching control signals (46) to the inverter switching devices of eachinverter output phase according to a corresponding one of a plurality ofX carriers in each of a plurality of inverter pulse width modulationcycles to convert DC power into multiphase AC output power to drive anassociated motor load, each carrier being phase shifted by a non-zeroangle 360°/X relative to one another, X being an integer number ofinverter output phases of the multiphase inverter; and at least oneprocessor operative to: convert each of four sets of multiphase inverteroutput current samples obtained at four different sample times in agiven inverter pulse width modulation cycle into a corresponding pair ofstationary reference frame current values, and compute an estimatedrotor position associated with the motor load for the given inverterpulse width modulation cycle at least partially according to thestationary reference frame current values for the given inverter pulsewidth modulation cycle.
 9. The motor drive of claim 8, wherein the foursets of multiphase inverter output current samples are sampledapproximately at 90° intervals in the given inverter pulse widthmodulation cycle.
 10. The motor drive of claim 8, wherein the four setsof multiphase inverter output current samples are sampled approximatelyat peaks, valleys and mid-points of one of a plurality of one of thecarriers in the given inverter pulse width modulation cycle.
 11. Themotor drive of claim 8, wherein the at least one processor is operativeto: compute the estimated rotor position θ for the given inverter pulsewidth modulation cycle according to α-β stationary reference framecurrent value pairs i_(α)(t_(i)), i_(β)(t_(i)) for the four sample timest_(i) where i=1-4 according to the following equation:${\theta = {0.5\mspace{14mu} {\tan^{- 1}\left( \frac{u(1)}{u(2)} \right)}}},{{where}\text{:}}$${{u(1)} = {{- \left( {i_{\alpha \; 2} + i_{\beta \; 1}} \right)} = {- \frac{4\; V_{h}\left( {L_{1}\mspace{14mu} \sin \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}}, {{u(2)} = {{i_{\beta \; 2} - i_{\alpha \; 1}} = {- \frac{4\; V_{h}\left( {L_{1}\mspace{14mu} \cos \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}}, {and}$i_(α1) = i_(α)(t₁) − i_(α)(t₃), i_(β 1) = i_(β)(t₁) − i_(β)(t₃), i_(α 2) = i_(α)(t₂) − i_(α)(t₄), andi_(β 2) = i_(β)(t₂) − i_(β)(t₄).
 12. A method for estimating a rotorposition of a motor load driven by an inverter, the method comprising:using at least one processor, converting each of four sets of multiphaseinverter output current samples obtained at four different sample timesin a given inverter pulse width modulation cycle into a correspondingpair of stationary reference frame current values; and using the atleast one processor, computing an estimated rotor position for the giveninverter pulse width modulation cycle at least partially according tothe stationary reference frame current values for the given inverterpulse width modulation cycle.
 13. The method of claim 12, comprisingsampling the four sets of multiphase inverter output current samplesapproximately at 90° intervals in the given inverter pulse widthmodulation cycle.
 14. The method of claim 13, comprising sampling thefour sets of multiphase inverter output current samples approximately atpeaks, valleys and mid-points of one of a plurality of phase shiftedcarriers used in the given inverter pulse width modulation cycle tooperate the inverter.
 15. The method of claim 12, comprising samplingthe four sets of multiphase inverter output current samplesapproximately at peaks, valleys and mid-points of one of a plurality ofphase shifted carriers used to operate the inverter in the giveninverter pulse width modulation cycle.
 16. The method of claim 12,comprising: computing the estimated rotor position θ for the giveninverter pulse width modulation cycle according to α-β stationaryreference frame current value pairs i_(α)(t_(i)), i_(β)(t_(i)) for thefour sample times t_(i) where i=1-4 according to the following equation:${\theta = {0.5\mspace{14mu} {\tan^{- 1}\left( \frac{u(1)}{u(2)} \right)}}},{{where}\text{:}}$${{u(1)} = {{- \left( {i_{\alpha \; 2} + i_{\beta \; 1}} \right)} = {- \frac{4\; V_{h}\left( {L_{1}\mspace{14mu} \sin \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}}, {{u(2)} = {{i_{\beta \; 2} - i_{\alpha \; 1}} = {- \frac{4\; V_{h}\left( {L_{1}\mspace{14mu} \cos \; 2\; \theta} \right)}{\omega_{h}\left( {L_{0}^{2} - L_{1}^{2}} \right)}}}}, {and}$i_(α1) = i_(α)(t₁) − i_(α)(t₃), i_(β 1) = i_(β)(t₁) − i_(β)(t₃), i_(α 2) = i_(α)(t₂) − i_(α)(t₄), andi_(β 2) = i_(β)(t₂) − i_(β)(t₄).
 17. The method of claim 16,comprising sampling the four sets of multiphase inverter output currentsamples approximately at 90° intervals in the given inverter pulse widthmodulation cycle.
 18. The method of claim 16, comprising sampling thefour sets of multiphase inverter output current samples approximately atpeaks, valleys and mid-points of one of a plurality of phase shiftedcarriers used in the given inverter pulse width modulation cycle tooperate the inverter.
 19. A non-transitory computer readable medium withcomputer executable instructions for estimating a rotor position of amotor load driven by an inverter, comprising computer executableinstructions for: converting each of four sets of multiphase inverteroutput current samples obtained at four different sample times in agiven inverter pulse width modulation cycle into a corresponding pair ofstationary reference frame current values; and computing an estimatedrotor position for the given inverter pulse width modulation cycle atleast partially according to the stationary reference frame currentvalues for the given inverter pulse width modulation cycle.
 20. Thenon-transitory computer readable medium of claim 19, comprising computerexecutable instructions for sampling the four sets of multiphaseinverter output current samples approximately at peaks, valleys andmid-points of one of a plurality of phase shifted carriers used in thegiven inverter pulse width modulation cycle to operate the inverter.